according to the IRS.gov website *today*, first round completed by may 2. second round completed by may 9, third round completed by may 16.
details here:
Stimulus Payment Schedule for Tax Returns Processed by April 15
(too much speculation going around...lots of misinformation, caused in large part by the change in schedule by the IRS. just go to the source to find out when to expect the money, if you qualify.)